The Premier League champions have stepped up their pursuit by opening negotiations with Aston Villa, according to the Guardian.
Grealish is expected to hold crunch talks over his future club’s hierarchy when he reports back for pre-season training next week.
The 25-year-old midfielder has been on holiday in Mykonos after helping England reach the Euro 2020 final.
Villa have no desire to sell their 25-year-old talisman unless a British record £100m valuation is met and will offer him a bumper new contract worth more than £150,000 a week in an effort to convince him to stay.
But if Grealish indicates that he wants to leave then City are expected to offer around £75m plus add-ons as Pep Guardiola attempts to prise away one of English football’s biggest talents.
However, City are determined to press for a player long admired by Guardiola in the hope an agreement can be reached swiftly.
Grealish signed a new contract at Villa in September after being courted by Manchester United.
There has been much speculation of a £100m buyout clause in that deal although neither side have ever confirmed its existence.
Yet there is a growing acceptance that that figure must be met by City before they can team Grealish in a dream midfield with his favourite Premier League player Kevin De Bruyne.
Sportsmail revealed in March that City had emerged as frontrunners for Grealish’s signature and they still hold out hope they can sign £150m-rated Harry Kane from Tottenham also.
City have £45m from the sale of Leroy Sane to Bayern Munich last year and have raised around £50m from the sale of fringe players this summer.
More are due to be sold while there is an acceptance that the likes of Bernardo Silva could yet leave before the end of the window to further offset their outlay.
The signing of Grealish would be a real statement of intent as they look to retain the title and go one step further in the Champions League.
For their part, Villa have been working to strengthen their own squad regardless.
They signed Emi Buendia from Norwich City for £33m, Ashley Young on a free and have had a £25m bid rejected for Bayer Leverkusen winger Leon Bailey as they continue to assemble a squad that can challenge for European qualification.